Orbital velocity and gravity calculator

Orbital velocity and period, escape velocity, surface gravity, your weight on the Moon or Mars, and the gravitational force between two masses.

Mis à jour 28 septembre 2026Exemples vérifiés : 8

Orbital speed

m/s

Chiffres significatifs : 6 ; Au plus proche, égalités en s’éloignant de zéro

Orbital period: 1 h 32 min 24 s / 1.54023h
Altitude above the surface: 400km
Orbit radius from the centre: 6,771km
Escape velocity from that altitude: 10,850.7m/s
Gravitational parameter GM: 3.98603 × 10¹⁴m³/s²

G is known to about 2 parts in 100,000 (CODATA 2022), so the last one or two significant figures shown are uncertain.

A circular orbit 400 km above Earth needs 7.6726 km/s and takes 92.414 minutes per lap. Mass of the satellite doesn't matter.

Orbit around Earth to scale (km)

Comment le calcul est effectué S

Gravitational parameter
$GM = (6.67430\times10^{-11})(5.9722 \times 10^{24}) = 398{,}603{,}000{,}000{,}000\ \mathrm{m^3/s^2}$
Kepler's third law
$T = 2\pi\sqrt{\frac{r^3}{GM}} = 2\pi\sqrt{\frac{(6{,}771{,}000)^3}{398{,}603{,}000{,}000{,}000}} = 5{,}544.84\ \mathrm{s} = 1.54023\ \mathrm{h}$
Circular orbit speed
$v = \sqrt{\frac{GM}{r}} = \sqrt{\frac{398{,}603{,}000{,}000{,}000}{6{,}771{,}000}} = 7{,}672.62\ \mathrm{m/s}$

À propos de Orbital velocity and gravity calculator

Newton's law of gravitation, F = Gm₁m₂/r², gives the pull between two masses. For a body of mass M the same law sets the speed of a circular orbit, v = √(GM/r), its period from Kepler's third law, T = 2π√(r³/GM), the escape velocity √(2GM/r) and the surface gravity GM/R². Pick the Earth, Moon, Mars, Jupiter or the Sun, or enter any mass and radius.

The default, an orbit 400 km above Earth like the International Space Station's, gives 7.67 km/s (about 17,200 mph) and 92.4 minutes per lap. Entering one sidereal day, 23.934 hours, as the period returns the geostationary radius of 42,164 km.

Radii are volumetric means from NASA's fact sheets and rotation is ignored, so Earth's surface gravity comes out at 9.82 m/s², between the 9.78 m/s² measured at the equator and 9.83 m/s² at the poles. Orbits are circular and drag-free.

Exemples détaillés

ISS-like orbit at 400 km

Calculate: Circular orbit
Corps: Earth
Given: Altitude → speed and period
Altitude above the surface: 400 km
Unité des résultats: km, m/s, N

Orbital speed: 7,672.62 m/s
Orbital period: 1.54023 h

Source de vérification : Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h

Geostationary altitude from one sidereal day

Calculate: Circular orbit
Corps: Earth
Given: Period → altitude
Orbital period: 23.9344696 h
Unité des résultats: km, m/s, N

Altitude above the surface: 35,793.2 km
Orbital speed: 3,074.67 m/s

Source de vérification : Python 3.8 decimal: r = (GM T²/4π²)^⅓ = 42164.2 km (the published GEO radius); minus the 6371 km mean radius (35,786 km is quoted above the 6378 km equatorial radius)

Orbit skimming the surface (altitude 0)

Calculate: Circular orbit
Corps: Earth
Given: Altitude → speed and period
Altitude above the surface: 0 km
Unité des résultats: km, m/s, N

Orbital speed: 7,909.81 m/s

Source de vérification : Python 3.8 decimal: √(GM/R) with R = 6371.0 km = 7909.813

Escape velocity from Earth's surface

Calculate: Escape velocity
Corps: Earth
Altitude above the surface: 0 km
Unité des résultats: km, m/s, N

Escape velocity from that altitude: 11,186.2 m/s

Source de vérification : Python 3.8 decimal: √(2GM/R) = 11186.165 m/s (NASA fact sheet lists 11.186 km/s)

Questions

How fast does the International Space Station orbit Earth?

About 7.67 km/s at 400 km altitude, which is 27,600 km/h or roughly 17,200 mph, and one lap takes 92.4 minutes. The speed depends only on Earth's GM and the orbit radius (6,771 km here), not on the station's mass. Raising the orbit to 410 km slows it by 5.7 m/s and lengthens the lap by 12 seconds.

What is the escape velocity of Earth?

11.186 km/s from the surface, about 40,270 km/h, the figure on NASA's Earth fact sheet. It is the speed at which an unpowered object never falls back, ignoring air drag, and it is the same for a pebble and a rocket. The Moon's is 2.38 km/s, Mars's 5.03 km/s and Jupiter's about 60 km/s. From 400 km up it drops to 10.85 km/s.

Why is escape velocity √2 times orbital velocity?

Escaping takes twice the kinetic energy of a circular orbit at the same height. In a circular orbit the kinetic energy is GMm/2r; reaching infinity needs GMm/r, the full depth of the potential well. Doubling kinetic energy multiplies speed by √2 ≈ 1.414, so the 7.67 km/s orbital speed at 400 km above Earth becomes an escape speed of 10.85 km/s.

How high is a geostationary orbit?

35,786 km above the equator, a radius of 42,164 km from Earth's centre. At that radius Kepler's third law gives a period of one sidereal day, 23 h 56 min 4 s, so the satellite keeps pace with Earth's rotation. Entering that period here gives the same radius and an altitude of 35,793 km, because the calculator subtracts the 6,371 km mean radius rather than the 6,378 km equatorial radius.

How much would I weigh on the Moon or Mars?

About 16.6% of your Earth weight on the Moon and 38% on Mars. Surface gravity GM/R² is 1.62 m/s² on the Moon and 3.73 m/s² on Mars with NASA's mean radii, against the 9.80665 m/s² standard gravity defined for Earth. A 70 kg person weighs 113.7 N on the Moon, which a scale calibrated on Earth would show as 11.6 kg.

Quelle est la précision de « Orbital velocity and gravity calculator » ?

La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 8. Par exemple, « ISS-like orbit at 400 km » est vérifié à l’aide de Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h.

D’où vient cette méthode ?

OpenStax University Physics Volume 1, ch. 13 Gravitation (§13.5 Satellite orbits, §13.3 Escape velocity); CODATA 2022 — Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²; NASA Planetary Fact Sheets (mass, volumetric mean radius).

À propos de ce calculateur

F = \frac{Gm_1m_2}{r^2},\quad v = \sqrt{\frac{GM}{r}},\quad T = 2\pi\sqrt{\frac{r^3}{GM}},\quad v_{\text{esc}} = \sqrt{\frac{2GM}{r}},\quad g = \frac{GM}{R^2}

Sources

Vérifié avec les références

Ce calculateur comprend 8 exemples résolus dont les réponses proviennent de sources indépendantes. Ils font partie de la suite de tests et peuvent aussi être exécutés ici.